This is somewhat of a difficult question, as I have so very little experience with the practices of humanities scholars before the digital age. For today's students in developed (and even most developing) countries, computers are essential to our research and I would guess that most students would be hard pressed to get much research done should they find these tools inaccessible.
Our research starts with a cursory search in Google or Primo, and we've sat through guest lectures on how to expand or narrow our search results to find a suitable breadth of scholarship. We've all been taught to take the unsourced John Q. Geocities "10 Things You Didn't Know about the French Revolution!" page with a grain of salt, yet to make good use out of resources available on university or government websites - such as census information.
From there, we either access entirely digital journal articles and books, or we use the library's digital tracking system to check the current availability and location of "real" books in meatspace. If the above fails, we have the tools to request digital or physical volumes through Trellis, most of which can be done without ever speaking to another person. We don't even need to guess the arrival date, as we'll get an e-mail telling us when our requests have been fulfilled.
School and classroom administration are increasingly digital as well, as transcripts are only a login and a few menu clicks away, as are past grades, financial information, and the ability to add or drop courses as one desires. I've honestly no idea how students registered for courses before the internet, but I know well that rituals have already grown around the system in place now, where students hover over their keyboards like hungry scavengers, waiting for the exact moment course selection opens up for their window so that they might claim a spot in a popular or needed course.
As far as the future is concerned, I have little doubt that we will see the digital aspect of academia expand greatly. Perhaps the most significant aspect is the trend towards entirely online courses, something which challenges many of the fundamental characteristics of academia in ways that could be seen as liberating, cheapening, somewhere between the two, or something else entirely.
My greatest hope, and goal, is to use digital tools and approaches to bring academia to a wider audience. I think tools such as blogs or podcasts are increasingly employed by more and more professionals (as well as amateurs) who want to share something without the constraints of academia. It's certainly worth considering that this accessibility comes with costs – not the least of which the lack of peer-review that needs to happen to upload a new podcast, or for a new blog post to publish.
I am not too sure what solutions could exist for something like that, though I suspect it wouldn't be as much an issue as it first seems. Unsourced news reports are far from unique to the internet, and people like Alex Jones will always find an audience of people who couldn't be bothered to seek out a second opinion. This may be a bit optimistic, but simply having these discussions in open digital spaces for anyone with interest to discover just might help to condition new generations born into the digital world to recognize that there are many difference voices speaking on a given issue, and that we can look at the evidence they give to measure their validity.
That, or the work of future professors becomes building powerpoints and answering angry e-mails.